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In this article, a model predictive current controller for multilevel inverters driving electrical machines is proposed. The inverter switch positions are directly set by the controller, thus avoiding the use of a modulator. Admissible switching sequences are enumerated, and a state-space model of the drive is used to predict the drive's response to each sequence. The predicted short-term switching losses are evaluated and minimized. The concept of extrapolation and the use of bounds achieve an effective prediction horizon of up to 100 time steps despite the short switching horizon.